Abstract
A method for determining the orbit types of the action of the group of gauge transformations on the space of connections for gauge theories with gauge group SU(n) in spacetime dimension d≤4 is presented. The method is based on the one-to-one correspondence between orbit types and holonomy-induced reductions of the underlying principal SU(n)-bundle. It is shown that the orbit types are labelled by certain cohomology elements of spacetime satisfying two relations. Thus, for every principal SU(n)-bundle the corresponding stratification of the gauge orbit space can be explicitly determined. As an application, a criterion characterizing kinematical nodes for physical states in Yang–Mills theory with the Chern–Simons term proposed by Asorey et al. is discussed.
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Rudolph, G., Schmidt, M. & Volobuev, I.P. Classification of Gauge Orbit Types for SU(n)-Gauge Theories. Mathematical Physics, Analysis and Geometry 5, 201–241 (2002). https://doi.org/10.1023/A:1020968206969
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DOI: https://doi.org/10.1023/A:1020968206969